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User blog:Granpa/Natural units
Fundamental units: *Time *Space *Mass *Charge Stoney units are defined by: : = e'' = ''k = 1}}, Planck units are defined by : = ''k = 1}}, where: * is the speed of light, * is the reduced Planck constant, * is the gravitational constant, * }} is the Coulomb constant, * is the Boltzmann constant * is the elementary charge, Summary table where: * is the fine-structure constant * }} is the gravitational coupling constant * is proton-to-electron mass ratio Some equivalent definitions of in terms of other fundamental physical constants are: : \alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar} = \frac{k_\text{e} e^2}{\hbar c} = \frac{c \mu_0}{2 R_\text{K}} = \frac{e^2}{4 \pi}\frac{Z_0}{\hbar} where: * is the elementary charge; * is the mathematical constant pi; * is the reduced Planck constant; * is the speed of light in vacuum; * is the electric constant or permittivity of free space; * is the magnetic constant or permeability of free space; * is the Coulomb constant; * is the von Klitzing constant; * is the vacuum impedance or impedance of free space. is typically defined in terms of the gravitational attraction between two electrons. More precisely, : \alpha_\mathrm{G} = \frac{G m_\mathrm{e}^2}{\hbar c} = \left( \frac{m_\mathrm{e}}{m_\mathrm{P}} \right)^2 \approx 1.751751596 \times 10^{-45} where: * is the gravitational constant; * is the electron rest mass; * is the speed of light in vacuum; * is the reduced Planck constant; * is the Planck mass. The Boltzmann constant, , is a scaling factor between macroscopic (thermodynamic temperature) and microscopic (thermal energy) physics. Macroscopically, the ideal gas law states: : p V = N k T , where: * is the number of molecules of gas. Energy has a different dimension from temperature. It is calculated as the product of the Boltzmann constant and temperature: * E = k_B T . Average energy per degree of freedom is kT}}. Electromagnetism Gravitoelectromagnetism According to general relativity, the gravitational field produced by a rotating object (or any rotating mass–energy) can, in a particular limiting case, be described by equations that have the same form as in classical electromagnetism. Starting from the basic equation of general relativity, the Einstein field equation, and assuming a weak gravitational field or reasonably flat spacetime, the gravitational analogs to Maxwell's equations for electromagnetism, called the "GEM equations", can be derived. GEM equations compared to Maxwell's equations in SI units are: where: * E'g is the static gravitational field (conventional gravity, also called ''gravitoelectric in analogous usage) in m⋅s−2; * '''E is the electric field; * B'''g is the gravitomagnetic field in s−1; * '''B is the magnetic field; * ρ''g is mass density in kg⋅m−3; * ''ρ is charge density: * J'g is mass current density or mass flux ('J'g = ''ρ''g'vρ, where v'''ρ is the velocity of the mass flow generating the gravitomagnetic field) in kg⋅m−2⋅s−1; * '''J is electric current density; * G'' is the gravitational constant in m3⋅kg−1⋅s−2; * ''ε''0 is the vacuum permittivity; * ''c is the speed of propagation of gravity (which is equal to the speed of light according to general relativity) in m⋅s−1. CGS References Category:Blog posts